G1 Focusing question

I'm very much enjoying playing with my new G1 (+ twin kit lenses), it seems very capable, and satisfying to use.

A couple of questions.

1. Forgive me if this is an obvious one, am I right in thinking that if I focus , and then zoom in or out the focus stays at the same distance?, i.e. Unlike my FZ5 which needs to refocus when you zoom.

2. Out of curiousity what is all the weird faint whirring going on all the time within the camera? I can turn off OIS and AF and its still there if you put you ear to the camera. It sounds very busy and it must be using battery juice.